Final answer:
To convert 5 × 4 4/5π radians to degrees, we express 4 4/5 as an improper fraction, multiply by 5 to find the radian measure, then convert to degrees using the factor 1 radian ≈ 57.3°. After the calculation, the result is approximately 240°.
The correct option is 4.
Step-by-step explanation:
To convert 5 × 4 4/5π radians to degrees, first simplify the mixed number 4 4/5 to an improper fraction. The fraction 4 4/5 is equivalent to (4 × 5 + 4)/5, which simplifies to 24/5.
Next, multiply 5 by 24/5π to find the radian measure, which is 24π. Now, we can use the conversion factor 1 radian ≈ 57.3° to convert radians to degrees:
24π radians × (57.3° / 1 radian) = 24 × 3.14159 × 57.3° = 432π degrees / 1 radian.
Then, calculate 432π degrees, knowing that π is approximately 3.14159:
432 × 3.14159 = 1357.16808°
Lastly, we can identify the closest answer choice:
240°
Since 1357.16808° is closest to 1368° (which is 240° when reduced within a single revolution), the approximate answer to the conversion of 5 × 4 4/5π radians to degrees is 240°.
The correct option is 4.